Donald Trump hasn't put California über alles—focusing instead on his home state of New York—a move that could spell trouble for the Republican front-runner in June, when 172 delegates from the Golden State come up for grabs in the Republican presidential primary.

A new Field poll shows that, while Trump leads statewide, he trails Senator Ted Cruz 40 percent to 29 percent in Los Angeles County, where 18 of the state's 53 congressional districts are located.

California awards the majority of its delegates on a winner-take-all basis by congressional district. Each of the state's 53 districts have three delegates to award, for 159 total. The remaining 13 delegates are awarded winner-take-all by statewide totals.

If Cruz's lead in Los Angeles County holds until June, he could walk away with 53 delegates, or about a third of the state's total allocation. According to the poll, Cruz also leads Trump 42-33 in the state's Central Valley and High Sierra regions. Those areas have fewer delegates to award than L.A., but Cruz could still squeeze delegates in the double-digits from them.

That's bad news for Trump, who needs big, decisive wins in delegate-rich states like California and New York if he hopes to rack up the 1,237 delegates he needs to avoid a contested convention in July.

"While the poll cannot estimate who is leading within each congressional district, it does show that Trump is leading in two regions, while Cruz leads in two others. Should these regional differences persist, it would dilute the delegate advantages accrued by the winner of the June 7 California primary," says Mark DiCamillo, director of the Field poll.

The poll shows Trump ahead of Cruz in the San Francisco Bay Area 39 percent to 32 percent, but the sample size for that area is smaller than the others.

If Trump enters July without the 1,237 delegates needed to clinch the nomination, there is a chance that Cruz, John Kasich or somebody else could become the Republican nominee through parliamentary finagling, despite the fact that Trump is almost guaranteed to have the most delegates overall. Trump has said such an outcome could lead to "riots."

The Field poll sampled 1,400 registered voters in California, including 558 likely Republican voters. The margin of error for all voters was plus-or-minus 3.2 points. For Republicans, it was plus-or-minus four points.